The present invention pertains generally to devices and methods for separating particles according to their mass. More particularly, the present invention pertains to devices and methods which rely on the orbital mechanics of charged particles, under the influence of a magnetic field in a low collisional density environment, to separate the particles from each other. The present invention is particularly, but not exclusively, useful for separating ions having a low mass to charge ratio from ions having a high mass to charge ratio in a multi-species plasma.
There are many reasons why it may be desirable to separate or segregate mixed materials from each other. Indeed, many different types of devices, which rely on different physical phenomena, have been proposed for this purpose. For example, settling tanks which rely on gravitational forces to remove suspended particles from a solution and thereby segregate the particles are well known and are commonly used in many applications. As another example, centrifuges which rely on centrifugal forces to separate substances of different densities are also well known and widely used. In addition to these more commonly known methods and devices for separating materials from each other, there are also devices which are specifically designed to handle special materials. A plasma centrifuge is an example of such a device.
As is well known, a plasma centrifuge is a device which generates centrifugal forces that separate charged particles in a plasma from each other. For its operation, a plasma centrifuge necessarily establishes a rotational motion for the plasma about a central axis. A plasma centrifuge also relies on the fact that charged particles (ions) in the plasma will collide with each other during this rotation. The result of these collisions is that the relatively high mass ions in the plasma will tend to collect at the periphery of the centrifuge. On the other hand, these collisions will generally exclude the lower mass ions from the peripheral area of the centrifuge. The consequent separation of high mass ions from the relatively lower mass ions during the operation of a plasma centrifuge, however, may not be as complete as is operationally desired, or required.
Apart from a centrifuge operation, it is well known that the orbital motions of charged particles (ions) which have the same velocity in a magnetic field, or in crossed electric and magnetic fields, will differ from each other according to their respective masses. Thus, when the probability of ion collision is significantly reduced, the possibility for improved separation of the particles due to their orbital mechanics is increased. For example, U.S. application Ser. No. 09/192,945 which was filed on Nov. 16, 1998, by Ohkawa for an invention entitled xe2x80x9cPlasma Mass Filterxe2x80x9d and which is assigned to the same assignee as the present invention discloses a device which relies on the different orbital motions of charged particles in a low density environment to separate the charged particles from each other. As implied above, In order to do this the plasma must be generated under low density conditions where the collisionality of the plasma is low. For purposes of the present invention, the collisionality of the plasma is considered to be low when the ratio of ion cyclotron frequency to ion collisional frequency is approximately equal to one, or is greater than one.
As indicated above, plasma centrifuges require a rotational motion of the plasma in order to generate centrifugal forces that are required for separating particles in the plasma from each other. To generate such a motion, centrifuges have typically used an inwardly directed axisymmetric radially oriented electric field. Heretofore, however, the plasma densities have been maintained relatively high in order to achieve a maximum throughput. With very low densities, however, and particularly densities that have very low collisionality, the orbital mechanics of charged particles can be advantageously used to separate the particles from each other according to their respective masses. Consequently, as more thoroughly indicated in the mathematics set forth below, when the collisionality of a plasma is low, charged particles in the plasma, which have different masses, can be distinguished by their respective orbits. Furthermore, when an axisymmetric electric field is employed in a low collision density environment, an inwardly directed electric field can assist in the process of separation. However, in contrast to both the plasma centrifuge and the plasma mass filter, the heavy particles are preferentially located at small radius.
Consider now the parameters that are involved for a cylindrical plasma mass filter when the ionization region extends from rin to rout. Also consider that none of the orbits of the light ions may extend farther in than the collector radius rcoll, not even those with the highest mass to charge (M1) that start at the smallest radius (rin). All of the orbits of the heavy ions must extend in at least as far as the collector radius rcoll, even those with the lowest mass to charge (M2) that start at the largest radius (rout).
It can be shown that the turning points r0,1 for an arbitrary potential xcfx86(r) are given by                                           8            ⁢                          mr                              0                ,                1                            2                                                          q              2                        ⁢                          B              2                                      ⁢                  (                      W            -                          q              ⁢                              xe2x80x83                            ⁢                              φ                ⁢                                  (                                      r                                          0                      ,                      1                                                        )                                                              )                    -                        (                                    r                              0                ,                1                            2                        -                                          2                ⁢                L                            qB                                )                2              =    0    ,
where W is the total energy (kinetic plus potential) and L is the canonical angular momentum (mechanical plus magnetic), both constants of the motion. If the particle is at rest at r0 (because the ionization occurs there), then the energy is W=qxcfx86(r0) and the canonical angular momentum is L=qBr02/2, so that                                           8            ⁢                          mr              1              2                                            qB            2                          ⁢                  (                                    φ              ⁢                              (                                  r                  0                                )                                      -                          φ              ⁢                              xe2x80x83                            ⁢                              (                                  r                  1                                )                                              )                    -                        (                                    r              1              2                        -                          r              0              2                                )                2              =    0    ,
or                     8        ⁢        m        ⁢                  xe2x80x83                ⁢        Δ        ⁢                  xe2x80x83                ⁢                  φ                      0            -            1                                                qB          2                ⁢                  r          0          2                      =                  (                                            r              1                                      r              0                                -                                    r              0                                      r              1                                      )            2        ,
where we have defined the potential drop xcex94xcfx860xe2x88x921=xcfx86(r0)xe2x88x92xcfx86(r1), which is always positive.
In an inverted filter, the ions with mass mh born at rout turn around again at rcoll, so we have             8      ⁢              m        h            ⁢              Δφ                  out          ⁢                      -                    ⁢          coll                                    qB        2            ⁢              r        out        2              =                    (                                            r              out                                      r              coll                                -                                    r              coll                                      r              out                                      )            2        .  
If the potential drop and machine size are fixed by practical considerations, the magnetic field can be made large if rcoll≈rout. A large field improves throughput by allowing a larger density before collisionality degrades performance, but this would be offset by the decreased area available between rcoll and rout. A practical compromise and the preferred embodiment, subject to optimization in a detailed design, is to use half the area for plasma, implying rcoll=rout/{square root over (2)} and             8      ⁢              m        h            ⁢              Δφ                  out          ⁢                      -                    ⁢          coll                                    qB        2            ⁢              r        out        2              =            1      2        .  
Another important question is the allowed radial extent of the source. A separator will not be practical if the ionization must be confined to too narrow a region. Applying the formula derived above to ions with mass ml born at rin, which must also turn around again at rcoll, we have                     8        ⁢                  m          l                ⁢                  Δφ                      in            ⁢                          -                        ⁢            coll                                                qB          2                ⁢                  r          in          2                      =                  (                                            r              in                                      r              coll                                -                                    r              coll                                      r              in                                      )            2        ,
or                     m        l            ⁢      Δ      ⁢              xe2x80x83            ⁢              φ                  in          ⁢                      -                    ⁢          coll                                    m        h            ⁢      Δ      ⁢              xe2x80x83            ⁢              φ                  out          ⁢                      -                    ⁢          coll                      =                              (                                                    (                                                      r                    in                                                        r                    coll                                                  )                            2                        -            1                    )                2                              (                                                    (                                                      r                    out                                                        r                    coll                                                  )                            2                        -            1                    )                2              .  
Given the form of the potential, the masses, and (rout/rcoll), this equation determines how much room can be allowed for ionization (routxe2x88x92rin).
The normal axisymmetric plasma mass filter has xcfx86(r) proportional to r2 . If we insert this potential profile into the equation above, we find                     (                              m            l                    ⁢                      (                                                            (                                                            r                      in                                                              r                      coll                                                        )                                2                            -              1                        )                          )                              m          h                ⁢                  (                                                    (                                                      r                    out                                                        r                    coll                                                  )                            2                        -            1                    )                      =                            (                                                    (                                                      r                    in                                                        r                    coll                                                  )                            2                        -            1                    )                2                              (                                                    (                                                      r                    out                                                        r                    coll                                                  )                            2                        -            1                    )                2              ,
or             (                        r          in                          r          coll                    )        2    =                              m          l                          m          h                    ⁢              (                                            (                                                r                  out                                                  r                  coll                                            )                        2                    -          1                )              +    1.  
In light of the above, it is an object of the present invention to provide a plasma mass filter which has an inwardly directed electric field. It is another object of the present invention to provide a plasma mass filter which employs an axisymmetric electric field to influence the movements of high mass charged particles toward a centrally located collector. Still another object of the present invention is to provide a plasma mass filter which will differentiate between the masses of the charged particles in the plasma independently of the initial positions and velocities of the particles. Yet another object of the present invention is to provide for a plasma mass filter which is simple effective to use, relatively easy to manufacture, and comparatively cost effective.
In accordance with the present invention, an inverted orbit plasma mass filter includes a cylindrical container that defines a longitudinal axis. The container surrounds a cylindrical collector that is oriented coaxially with the container. Together these components establish an annular shaped plasma chamber that is located between the container and the collector.
A plurality of magnetic coils are mounted on the outside of the container to surround the chamber and generate a substantially uniform magnetic field (B) in the chamber that is generally parallel to the longitudinal axis of the filter. Additionally, an electrode is mounted at one end of the cylindrical container to generate a radially oriented electric field (E) in the chamber. Importantly, the electric field is directed inwardly from the container toward the collector. As intended for the present invention, the electrode may either be a plurality of coaxially oriented rings or a spiral electrode. Further, an electrode can be mounted at both ends of the container, if desired.
A source for injecting a multi-species plasma into said chamber is provided which, for purposes of disclosure will include both charged particles of a relatively low mass (M1) and of a relatively high mass (M2). More technically, they are particles (M1) of relatively low mass to charge ratio and particles (M2) of relatively high mass to charge ratio. As indicated above, however, these terms will be used interchangeably herein. Specifically, the low mass particles (M1) will have a cyclotron frequency and will orbit in the magnetic field (B) and the electric field (E) with a cyclotron trajectory T1 which will depend on the initial radial position and velocity of the particles. Likewise, the particles of relatively high mass (M2) will have a cyclotron frequency, and a cyclotron trajectory T2 in the magnetic field (B) and electric field (E) which will also depend on the initial radial position and velocity of the particles. For the same initial radial position and velocity, T2 will be greater than T1 (T2 greater than T1).
It is an important aspect of the present invention that the multi-species plasma operates with a density less than the xe2x80x9ccollisional density.xe2x80x9d For purposes of the present invention, the xe2x80x9ccollisional densityxe2x80x9d is realized under conditions wherein a ratio between the cyclotron frequency of the charged particles and the collisional frequency of the particles in the chamber (i.e. ion-ion and ion-neutral collisions) is greater than approximately one.
Structurally, and operationally, several design dimensions for the filter of the present invention are of interest. Specifically, if the collector is located at a radial distance rcoll from the longitudinal axis, the multi-species plasma should be injected into the chamber between the radial distances rin and routFor the present invention the distances rin and rout are measured from the longitudinal axis and their relationship to each other and to rcoll is: rcoll is less than rin, and rin is less than rout, (rcoll less than rin less than rout).
Within the dimensional configuration defined above, consider the cyclotron trajectory of a relatively high mass particle M2 as it moves under the influence of the electric field (E) and magnetic field (B) from an initial radial position of rout. When the cyclotron trajectory T2, of the relatively higher mass particle M2 is greater than (routxe2x88x92rcoll), then substantially all of the high mass particles (M2) will move into contact with the collector, regardless of their respective initial positions between rin and rout. On the other hand, consider the cyclotron trajectory of a relatively low mass particle M1 from an initial radial position of rin. When the cyclotron trajectory T1, of the relatively lower mass particles M1 is less than the difference (rinxe2x88x92rcoll), then substantially none of the low mass particles (M1) will orbit into contact with the collector regardless of their initial position between rin and rout. These considerations, coupled with conditions that are desirable for high throughput, lead to a design for the filter of the present wherein it can be mathematically shown that rcoll is approximately equal to the square root of two times smaller than rout (rcoll≈rout/{square root over (2)}). Furthermore, the most desirable relationship between rin and rout is determined by the ratio of the masses of the heavy and light particles M2/M1. For example, when M2/M1 =2, then r2in approx=(xc2xe)r2out.